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Econ Study guide - PartA Formulas_to_Help_with_Final_Part_A...

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Part A Formulas_to_Help_with_Final_Part_A MSE = SSE/(n-k-1). Where k= number of independent va SST = SSyy MSR = SSR/k. Where k= number of independent variable You are given that: SUM(X) = 22 SUM(Y) = 34 UM(Y^2) = 246 SUM(XY) = 162 SUM(X^2) = 118 n = 5 Given the above data calculate: SSxx, SSyy, SSxy, S2x, S2y, b1, bo, SSE, MSE, Sb1, tcalc, SST, SSR, MSR, R2 (R Square), F. SSxx 21.2 14.8 12.4 5.3 3.7 0.59 4.23 7.55 2.52 0.34 1.7 14.8 7.25 7.25 0.49 2.88 S 2 x = SSxx/(n-1) S 2 y = SSyy/(n-1) SSR = (b1) 2 (SSxx) (This formula is for Simple R This “sample Final” is a good practice for some of the possible Answers (in same orde
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X Y XY 1 140 25 19600 625 3500 2 119 29 14161 841 3451 3 103 46 10609 2116 4738 4 91 70 8281 4900 6370 5 65 88 4225 7744 5720 6 29 112 841 12544 3248 7 24 128 576 16384 3072 n = 7 SUM 571 498.0 58293 45154 30099 Avg Xbar /Ybar 81.57 71.14 SSxy = -10523.57 b1 = -0.9 SSxx = 11715.71 bo = 144.41 SSE = 272.12 Se= 7.38 SSE/n-2 = 54.42 130 SSyy = 9724.86 27.64 = α 10% 0.97 48.43 /2= α 5% 2345.33 t (α/2,n-2) = 2.02 0.2 0.34 For confidence interval: 0.59 t (α/2,n-2) * Se * [1/n +(x0-xbar)2/SSxx)]1/2 = 8.71 36.35 18.94 For prediction interval: 1+1/n +(x0-xbar)2/SSxx = 1.34 1.16 t (α/2,n-2) * Se * [1+ 1/n +(x0-xbar)2/SSxx)]1/2 = 17.23 44.87 10.41 MSE = SSE/(n-k-1 SST = SSyy MSR = SSR/k. Wh X 2 Y 2 x 0 = y 0 hat= r 2 = x 0 -xbar = (x 0 -xbar) 2 = (x 0 -xbar) 2 /SSxx = 1/n +(x0-xbar) 2 /SSxx = [1/n +(x0-xbar) 2 /SSxx)] 1/2 = y 0 hat ± {t ( /2,n-2) * Se * [1/n +(x0-xbar)2/SSxx)]1/2}= α [1+ 1/n +(x0-xbar) 2 /SSxx)] 1/2 = hat ± {t ( /2,n-2) * Se * [1+ 1/n +(x0-xbar)2/SSxx)]1/2}= α S 2 x = SSxx/(n-1) S 2 y = SSyy/(n-1) SSR = (b1) 2 (SSxx
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Yhats Residuals (e) 18.66 6.34 37.52 -8.52 51.89 -5.89 62.67 7.33 86.03 1.97 118.36 -6.36 122.86 5.14 SSxx^1/2= 108.24 0.07 t= -13.18 1952.62 1620.81 1). Where k= number of independent varia 9724.86 9452.74 here k= number of independent variables. s b = x) (This formula is for Simple Regression o
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ANOVA df SS MS F Regression 1 ? ? ? Error ? 21.96 ? Total 4 29.2 ANSWERS (in same order as questions: ERROR=4-1=3 SSR=29.2-21.96=7.24 MSR=SSR/dfr=7.24 MSE=SSE/dfe=7.32 F=MSR/MSE=0.989 . Sample Final Econ 309 F09 Part B . Given the data above, calculate df E (d.f. for Error Row), SSR (Sum of Squares of Regres
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ssion), MSR, MSE, F, R 2 (R Square).
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Ken Black Prblm 14.1 X Y XY X^2 1 12 17 204 144 1 21 15 315 441 1 28 22 616 784 1 8 19 152 64 1 20 24 480 400 SUM 5 89 97 1767 1833 AVERAGE 17.8 19.4 SSxy = 40.4 SSxx = 248.8 Green Font: Our Work in Excel b1 = 0.16 bo = 16.51
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Blue Fill: From Student Sol Manual Press "Ctrl" + "~" to see the formulas we used, press them together again to go back to numbers.
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Ken Black Prblm 14.1 x y x^2 xy 1 12 17 144 204 1 21 15 441 315 1 28 22 784 616 1 8 19 64 152 1 20 24 400 480 SUM 5 89 97 1833 1767 AVE 17.8 19.4 SSxy= 40.4 SSxx= 248.8 b1= 0.16 b0= 16.51 Press "Ctrl" + "~" to see the formula press them together again to go bac
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as we used, ck to numbers.
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X Y 1 12 17 2 21 15 3 28 22 4 8 19 n = 5 20 24 SUM 89 97 X^2 XY 144 204 Xbar = 17.8 17.8 441 315 Ybar = 19.4 784 616 64 152 400 480 SUM 1833 1767 residuals Yhats e SSxy = 40.4 b1 = 0.16 18.46 -1.46 19.92 -4.92 SSxx = 248.8 bo = 16.51 21.06 0.94 17.81 1.19 19.76 4.24
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e^2 ABS(e) ABS(e) -1Se IF 2.13 1.46 -2.48 1 24.2 4.92 0.98 0 0.89 0.94 -3 1 1.42 1.19 -2.75 1 18 4.24 0.3 0 46.64 3 =# of negative [ABS(e)-1Se] = SSE 15.55 = SSE/(n-2) 15.55 = SSE/(n-2) n = 5 7.33 3.94 = Se = SEE 3.94 3.94 7.89 =2*Se =/= SSE/(n-2)
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ABS(e) - 2Se IF -6.43 1 -2.97 1 -6.94 1 -6.69 1 -3.64 1 5 =# of negative [ABS(e)-2Se] proportion within 0+/- 1Se = = = 0.6 = 60 % for normal data we expect 0.68 proportion within 0+/- 2Se = = = 1 = 100 % for normal data we expect 0.95
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x y x^2 1 138 26 19044 1 116 28 13456 1 100 44 10000 1 94 69 8836 1 62 91 3844 1 29 110 841 1 23 129 529 SUM 7 562 497 56550 AVE 80.29 71 8078.57 I am using here the approach SSxx = n(SA-AS), etc. to calculate b1 & bo SSxy = -10381 SSxx = 11429.43 SSyy = 9892 b1 = -0.91 bo = 143.92 First Method to Calculate r^2: The followong formula is for Simple Regression only: b1= rSy/Sx r = b1(Sx/Sy) r^2 = [b1(Sx/Sy)]^2 (b1^2)SSxx/SSyy = Where Sx = SQRT(SSxx/(n-1)) = (SSxx/(n-1))^.5 Sy = SQRT(SSyy/(n-1)) = (SSyy/(n-1))^.5
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